Question

The measures of the angles of a triangle are x, 2x, and 3x. How do you find the measure of each angle?

Answer 1

Hint: A triangle is a 2-dimensional shape containing 3 sides, and an angle is defined as the measure of turn between two sides. So a triangle has 3 angles and we are given the measure of each angle. We know that the sum of all the angles present in a triangle is equal to 180 degrees, so we will equate the sum of the given three angles to 180 degrees. And then solving the equation, we will get the correct answer.

Complete step-by-step solution:
We know that the sum of the three angles of a triangle is 180 degrees, so –
$
  x + 2x + 3x = 180^\circ \\
   \Rightarrow 6x = 180^\circ \\
   \Rightarrow x = \dfrac{{180^\circ }}{6} \\
   \Rightarrow x = 30^\circ \\
 $
So, one of the angles is of measure $30^\circ $ , other angles are 2 times and 3 times of this angle, so they are of the measure $60^\circ $ and $90^\circ $ respectively.
Hence, the measure of each angle is $30^\circ $ , $60^\circ $ and $90^\circ $

Note: We don’t know the measure of any angle in this question, they are represented by an unknown quantity x. When we formulate the equation using the angle sum property of the triangle, we see that the equation is an algebraic expression as it is a combination of both numerical values and alphabets. So it is solved by first adding all the terms containing x on the right-hand side and then we take 6 to the left-hand side to get the value of x. The obtained triangle is a right-angled triangle as one of its angles is of measure 90 degrees.